Are the NCTM Standards Suitable for Systematic Adoption?

The fundamental characteristic of mathematics is its abstraction. Its idealizations
have been found to give surprisingly accurate descriptions of phenomena in the real
world. Thus mathematics is endowed with incredible power to serve a broad range
of diverse areas. The same mathematical tools, differently interpreted, can be
applied to seemingly unrelated subjects to solve problems in a great variety of disciplines. Any educational program must address these important features of mathematics in a balanced way. One of the serious problems with the NCTM standards
is that the essence of the subject is lost. Problems are viewed as relevant and interesting to students only if they are related to familiar daily experiences. Unless they, are
tied in with theory, however, isolated problems may well fragment the discipline.
The power of mathematics vanishes when nothing occurs to show that the concrete is
an illustration of the abstract. We have a magnificent opportunity to enlighten our
students, leading them to the realization that mathematics is an intrinsically beautiful and exciting discipline in its own right. Its structure gives us substantial flexibility for teaching. We may use either the applications to develop the abstraction or,
conversely, start with the abstraction as a lead to application. By turning at various times in either direction, we can provide great mathematical enrichment for our
students.

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Deborah HaimoUniversity of California, San DiegoDeborah Tepper Haimo is currently at the University of California, San Diego. She is the co-author, with Richard Askey, of "Similarities Between Fourier & Power Series" (American Mathematical Monthly, 1996).